Answer:
volume of the bubble just before it reaches the surface is 5.71 cm³
Explanation:
given data
depth h = 36 m
volume v2 = 1.22 cm³ = 1.22 × [tex]10^{-6}[/tex] m³
temperature bottom t2 = 5.9°C = 278.9 K
temperature top t1 = 16.0°C = 289 K
to find out
what is the volume of the bubble just before it reaches the surface
solution
we know at top atmospheric pressure is about P1 = [tex]10^{5}[/tex] Pa
so pressure at bottom P2 = pressure at top + ρ×g×h
here ρ is density and h is height and g is 9.8 m/s²
so
pressure at bottom P2 = [tex]10^{5}[/tex] + 1000 × 9.8 ×36
pressure at bottom P2 =4.52 × [tex]10^{5}[/tex] Pa
so from gas law
[tex]\frac{P1*V1}{t1} = \frac{P2*V2}{t2}[/tex]
here p is pressure and v is volume and t is temperature
so put here value and find v1
[tex]\frac{10^{5}*V1}{289} = \frac{4.52*10^{5}*1.22}{278.9}[/tex]
V1 = 5.71 cm³
volume of the bubble just before it reaches the surface is 5.71 cm³
